Dynamic synapse for signal processing in neural networks

ABSTRACT

An information processing system having signal processors that are interconnected by processing junctions that simulate and extend biological neural networks. Each processing junction receives signals from one signal processor and generates a new signal to another signal processor. The response of each processing junction is determined by internal junction processes and is continuously changed with temporal variation in the received signal. Different processing junctions connected to receive a common signal from a signal processor respond differently to produce different signals to downstream signal processors. This transforms a temporal pattern of a signal train of spikes into a spatio-temporal pattern of junction events and provides an exponential computational power to signal processors. Each signal processing junction can receive a feedback signal from a downstream signal processor so that an internal junction process can be adjusted to learn certain characteristics embedded in received signals.

[0001] This application is a continuation application of U.S.application Ser. No. 09/096,678, filed Jun. 11, 1998 which claims thebenefit of the U.S. Provisional Application No. 60/049,758, filed onJun. 11, 1997.

FIELD OF THE INVENTION

[0002] The present invention relates to information processing by signalprocessors connected by processing junctions, and more particularly, toneural network models that simulate and extend biological neuralnetworks.

BACKGROUND OF THE INVENTION

[0003] A biological nervous system comprises a complex network ofneurons that receive and process external stimuli to produce, exchange,and store information. A neuron, in its simplest form as a basic unitfor a neural network, may be described as a cell body called soma,having one or more dendrites as input terminals for receiving signalsand one or more axons as output terminals for exporting signals. Thesoma of a neuron processes signals received from dendrites to produce atleast one action signal for transmission to other neurons via axons.Some neurons have only one axon which repeatedly splits branches,thereby allowing one neuron to communicate with multiple other neurons.

[0004] One dendrite (or axon) of a neuron and one axon (or dendrite) ofanother neuron are connected by a biological structure called a synapse.Hence, a neural network comprises a plurality of neurons that areinterconnected by synapses. Signals are exchanged and processed withinsuch a network.

[0005] Neurons also make anatomical and functional connections withvarious kinds of effector cells such as muscle, gland, or sensory cellsthrough another type of biological junctions called neuroeffectorjunctions. A neuron can emit a certain neurotransmitter in response toan action signal to control a connected effector cell so that theeffector cell reacts accordingly in a desired way, e.g., contraction ofa muscle tissue.

[0006] The structure and operations of a biological neural network areextremely complex. Many physical, biological, and chemical processes areinvolved. Various simplified neural models have been developed based oncertain aspects of biological nervous systems. See, Bose and Liang,“Neural network fundamentals with graphs, algorithms, and applications,”McGraw-Hill (1996). A brain, for example, is a complex system and can bemodeled as a neural network that processes information by the spatialand temporal pattern of neuronal activation.

[0007] One description of the operation of a general neural network isas follows. An action potential originated by a presynaptic neurongenerates synaptic potentials in a postsynaptic neuron. The somamembrane of the postsynaptic neuron integrates these synaptic potentialsto produce a summed potential. The soma of the postsynaptic neurongenerates another action potential if the summed potential exceeds athreshold potential. This action potential then propagates through oneor more axons as presynaptic potentials for other neurons that areconnected. The above process forms the basis for information processing,storage, and exchange in many neural network models.

[0008] Action potentials and synaptic potentials can form certaintemporal patterns or sequences as trains of spikes. The temporalintervals between potential spikes carry a significant part of theinformation in a neural network.

[0009] Another significant part of the information in a neural networkis the spatial patterns of neuronal activation. This is determined bythe spatial distribution of the neuronal activation in the network. Itis desirable to stimulate both the temporal and spatial patterns in aneural network model. See, for example, Deadwyler et al., “Hippocampalensemble activity during spatial delayed-nonmatch-to-sample performancein rats,” Journal of Neuroscience, Vol. 16, pp.354-372 (1996) and Thielset al., “Excitatory stimulation during postsynaptic inhibition induceslong-term depression in hippocampus in-vivo,” Journal of Neuroscience,Vol. 72, pp.3009-3016 (1994) and “NMDA receptor-dependent LTD indifferent subfields of hippocampus in vivo and in vitro,” Hippocampus,Vol. 6, pp. 43-51 (1996).

[0010] Many neural network models are based on the following twoassumptions. First, synaptic strength, i.e., the efficacy of a synapsein generating a synaptic potential, is assumed to be static during atypical time scale for generating an action potential in neurons. Theefficacy of a synapse is essentially a constant during a signal train.Certain models modify this assumption by allowing a slow variation overa period of processing many signal trains. In the second assumption,each sending neuron provides the same signal to all other neurons towhich it is synaptically connected.

SUMMARY OF THE INVENTION

[0011] One aspect of the present invention provides an improved neuralnetwork model that removes the above two assumptions and enables neuralnetwork devices to perform complex tasks. The present invention includesinformation processing systems and methods that are inspired by and areconfigured to extend certain aspects of a biological neural network. Thefunctions of signal processors and processing junctions connecting thesignal processors correspond to biological neurons and synapses,respectively. Each of the signal processors and processing junctions maycomprise any one or a combination of an optical element, an electronicdevice, a biological unit, or a chemical material. The processingsystems and methods may also be simulated by using one or more computerprograms.

[0012] Each processing junction is configured to dynamically adjust itsresponse strength according to the temporal pattern of an incomingsignal train of spikes. Hence, such a processing junction changes itsresponse to the incoming signal and hence simulates a “dynamic synapse”.

[0013] Different processing junctions in general respond differently tothe same input signal. This produces different output junction signals.This provides a specific way of transforming a temporal pattern of asignal train of spikes into a spatio-temporal pattern of junctionevents. In addition, the network of the signal processors and processingjunctions can be trained to learn certain characteristics embedded ininput signals.

[0014] One embodiment of a system for information processing includes aplurality of signal processors connected to communicate with one anotherand configured to produce at least one output signal in response to atleast one input signal, and a plurality of processing junctions disposedto interconnect the signal processors. Each of the processing junctionsreceives and processes a prejunction signal from a first signalprocessor in the network based on at least one internal junction processto produce a junction signal which causes a postjunction signal to asecond signal processor in the network. Each processing junction isconfigured so that the junction signal has a dynamic dependence on theprejunction signal.

[0015] At least one of the processing junctions may have anotherinternal junction process that makes a different contribution to thejunction signal than the internal junction process.

[0016] Each of the processing junctions may be connected to receive anoutput signal from the second signal processor and configured to adjustthe internal junction process according to the output signal.

[0017] These and other aspects and advantages of the present inventionwill become more apparent in light of the following detaileddescription, the accompanying drawings, and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018]FIG. 1 is a schematic illustration of a neural network formed byneurons and dynamic synapses.

[0019]FIG. 2A is a diagram showing a feedback connection to a dynamicsynapse from a postsynaptic neuron.

[0020]FIG. 2B is a block diagram illustrating signal processing of adynamic synapse with multiple internal synaptic processes.

[0021]FIG. 3A is a diagram showing a temporal pattern generated by aneuron to a dynamic synapse.

[0022]FIG. 3B is a chart showing two facilitative processes of differenttime scales in a synapse.

[0023]FIG. 3C is a chart showing the responses of two inhibitory dynamicprocesses in a synapse as a function of time.

[0024]FIG. 3D is a diagram illustrating the probability of release as afunction of the temporal pattern of a spike train due to the interactionof synaptic processes of different time scales.

[0025]FIG. 3E is a diagram showing three dynamic synapses connected to apresynaptic neuron for transforming a temporal pattern of spike traininto three different spike trains.

[0026]FIG. 4A is a simplified neural network having two neurons and fourdynamic synapses based on the neural network of FIG. 1.

[0027] FIGS. 4B-4D show simulated output traces of the four dynamicsynapses as a function of time under different responses of the synapsesin a simplified network of FIG. 4A.

[0028]FIGS. 5A and 5B are charts respectively showing sample waveformsof the word “hot” spoken by two different speakers.

[0029]FIG. 5C shows the waveform of the cross-correlation between thewaveforms for the word “hot” in FIGS. 5A and 5B.

[0030]FIG. 6A is schematic showing a neural network model with twolayers of neurons for simulation.

[0031]FIGS. 6B, 6C, 6D, 6E, and 6F are charts respectively showing thecross-correlation functions of the output signals from the outputneurons for the word “hot” in the neural network of FIG. 6A aftertraining.

[0032] FIGS. 7A-7L are charts showing extraction of invariant featuresfrom other test words by using the neural network in FIG. 6A.

[0033]FIGS. 8A and 8B respectively show the output signals from fouroutput neurons before and after training of each neuron to respondpreferentially to a particular word spoken by different speakers.

[0034]FIG. 9A is a diagram showing one implementation of temporal signalprocessing using a neural network based on dynamic synapses.

[0035]FIG. 9B is a diagram showing one implementation of spatial signalprocessing using a neural network based on dynamic synapses.

[0036]FIG. 10 is a diagram showing one implementation of a neuralnetwork based on dynamic synapses for processing spatio-temporalinformation.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0037] Certain aspects of the invention have been disclosed by Liaw andBerger in “Dynamic synapse: a new concept of neural representation andcomputation,” Hippocampus, Vol. 6, pp. 591-600 (1996); “Computing withdynamic synapse: a case study of speech recognition,” Proceedings ofInternational Conference on Neural Network, Houston, Tex., June of 1997;and “Robust speech recognition with dynamic synapses,” Proceedings ofthe International Joint Conference on Neural Network, Anchorage, Ak.,May of 1998. The disclosure of the above references are incorporatedherein by reference.

[0038] The following description uses terms “neuron” and “signalprocessor”, “synapse” and “processing junction”, “neural network” and“network of signal processors” in a roughly synonymous sense. Biologicalterms “dendrite” and “axon” are also used to respectively represent aninput terminal and an output terminal of a signal processor (i.e., a“neuron”).

[0039] A neural network 100 based on dynamic synapses is schematicallyillustrated by FIG. 1. Large circles (e.g., 110, 120, etc.) representneurons and small ovals (e.g., 114, 124, etc.) represent dynamicsynapses that interconnect different neurons. Effector cells andrespective neuroeffector junctions are not depicted here for sake ofsimplicity. The dynamic synapses each have the ability to continuouslychange an amount of response to a received signal according to atemporal pattern and magnitude variation of the received signal. This isdifferent from many conventional models for neural networks in whichsynapses are static and each provide an essentially constant weightingfactor to change the magnitude of a received signal.

[0040] Neurons 110 and 120 are connected to a neuron 130 by dynamicsynapses 114 and 124 through axons 112 and 122, respectively. A signalemitted by the neuron 110, for example, is received and processed by thesynapse 114 to produce a synaptic signal which causes a postsynapticsignal to the neuron via a dendrite 130 a. The neuron 130 processes thereceived postsynaptic signals to produce an action potential and thensends the action potential downstream to other neurons such as 140, 150via axon branches such as 131 a, 131 b and dynamic synapses such as 132,134. Any two connected neurons in the network 100 may exchangeinformation. Thus the neuron 130 may be connected to an axon 152 toreceive signals from the neuron 150 via, e.g., a dynamic synapse 154.

[0041] Information is processed by neurons and dynamic synapses in thenetwork 100 at multiple levels, including but not limited to, thesynaptic level, the neuronal level, and the network level.

[0042] At the synaptic level, each dynamic synapse connected between twoneurons (i.e., a presynaptic neuron and a postsynaptic neuron withrespect to the synapse) also processes information based on a receivedsignal from the presynaptic neuron, a feedback signal from thepostsynaptic neuron, and one or more internal synaptic processes withinthe synapse. The internal synaptic processes of each synapse respond tovariations in temporal pattern and/or magnitude of the presynapticsignal to produce synaptic signals with dynamically-varying temporalpatterns and synaptic strengths. For example, the synaptic strength of adynamic synapse can be continuously changed by the temporal pattern ofan incoming signal train of spikes. In addition, different synapses arein general configured by variations in their internal synaptic processesto respond differently to the same presynaptic signal, thus producingdifferent synaptic signals. This provides a specific way of transforminga temporal pattern of a signal train of spikes into a spatio-temporalpattern of synaptic events. Such a capability of pattern transformationat the synaptic level, in turn, gives rise to an exponentialcomputational power at the neuronal level.

[0043] Another feature of the dynamic synapses is their ability fordynamic learning. Each synapse is connected to receive a feedback signalfrom its respective postsynaptic neuron such that the synaptic strengthis dynamically adjusted in order to adapt to certain characteristicsembedded in received presynaptic signals based on the output signals ofthe postsynaptic neuron. This produces appropriate transformationfunctions for different dynamic synapses so that the characteristics canbe learned to perform a desired task such as recognizing a particularword spoken by different people with different accents.

[0044]FIG. 2A is a diagram illustrating this dynamic learning in which adynamic synapse 210 receives a feedback signal 230 from a postsynapticneuron 220 to learn a feature in a presynaptic signal 202. The dynamiclearning is in general implemented by using a group of neurons anddynamic synapses or the entire network 100 of FIG. 1.

[0045] Neurons in the network 100 of FIG. 1 are also configured toprocess signals. A neuron may be connected to receive signals from twoor more dynamic synapses and/or to send an action potential to two ormore dynamic synapses. Referring to FIG. 1, the neuron 130 is an exampleof such a neuron. The neuron 110 receives signals only from a synapse111 and sends signals to the synapse 114. The neuron 150 receivessignals from two dynamic synapses 134 and 156 and sends signals to theaxon 152. However connected to other neurons, various neuron models maybe used. See, for example, Chapter 2 in Bose and Liang, supra., andAnderson, “An introduction to neural networks,” Chapter 2, MIT (1997).

[0046] One widely-used simulation model for neurons is the integratormodel. A neuron operates in two stages. First, postsynaptic signals fromthe dendrites of the neuron are added together, with individual synapticcontributions combining independently and adding algebraically, toproduce a resultant activity level. In the second stage, the activitylevel is used as an input to a nonlinear function relating activitylevel (cell membrane potential) to output value (average output firingrate), thus generating a final output activity. An action potential isthen accordingly generated. The integrator model may be simplified as atwo-state neuron as the McCulloch-Pitts “integrate-and-fire” model inwhich a potential representing “high” is generated when the resultantactivity level is higher than a critical threshold and a potentialrepresenting “low” is generated otherwise.

[0047] A real biological synapse usually includes different types ofmolecules that respond differently to a presynaptic signal. The dynamicsof a particular synapse, therefore, is a combination of responses fromall different molecules. A dynamic synapse may be configured to simulatethe contributions from all dynamic processes corresponding to responsesof different types of molecules. A specific implementation of thedynamic synapse may be modeled by the following equations:${{P_{i}(t)} = {\sum\limits_{m}\quad {{K_{i,m}(t)}*{F_{i,m}(t)}}}},$

[0048] where P_(i)(t) is the potential for release (i.e., synapticpotential) from the ith dynamic synapse in response to a presynapticsignal, K_(i,m)(t) is the magnitude of the mth dynamic process in theith synapse, and F_(i,m)(t) is the response function of the mth dynamicprocess.

[0049] The response F_(i,m)(t) is a function of the presynaptic signal,A_(p)(t), which is an action potential originated from a presynapticneuron to which the dynamic synapse is connected. The magnitude ofF_(i,m)(t) varies continuously with the temporal pattern of A_(p)(t). Incertain applications, A_(p)(t) may be a train of spikes and the mthprocess can change the response F_(i,m)(t) from one spike to another.A_(p)(t) may also be the action potential generated by some otherneuron, and one such example will be given later. Furthermore,F_(i,m)(t) may also have contributions from other signals such as thesynaptic signal generated by dynamic synapse i itself, or contributionsfrom synaptic signals produced by other synapses.

[0050] Since one dynamic process may be different form another,F_(i,m)(t) may have different waveforms and/or response time constantsfor different processes and the corresponding magnitude K_(i,m)(t) mayalso be different. For a dynamic process m with K_(i,m)(t)>0, theprocess is said to be excitatory, since it increases the potential ofthe postsynaptic signal. Conversely, a dynamic process m withK_(i,m)(t)<0 is said to be inhibitory.

[0051] In general, the behavior of a dynamic synapse is not limited tothe characteristics of a biological synapse. For example, a dynamicsynapse may have various internal processes. The dynamics of theseinternal processes may take different forms such as the speed of rise,decay or other aspects of the waveforms. A dynamic synapse may also havea response time faster than a biological synapse by using, for example,high-speed VLSI technologies. Furthermore, different dynamic synapses ina neural network or connected to a common neuron can have differentnumbers of internal synaptic processes.

[0052] The number of dynamic synapses associated with a neuron isdetermined by the network connectivity. In FIG. 1, for example, theneuron 130 as shown is connected to receive signals from three dynamicsynapses 114, 154, and 124.

[0053] The release of a synaptic signal, R_(i)(t), for the above dynamicsynapse may be modeled in various forms. For example, the integratemodels for neurons may be directly used or modified for the dynamicsynapse. One simple model for the dynamic synapse is a two-state modelsimilar to a neuron model proposed by McCulloch and Pitts:${R_{i}(t)} = \left\{ \begin{matrix}0 & {{{{if}\quad {P_{i}(t)}} \leq \theta_{i}},} \\{f\left\lbrack {P_{i}(t)} \right\rbrack} & {{{{if}\quad {P_{i}(t)}} > \theta_{i}},}\end{matrix} \right.$

[0054] where the value of R_(i)(t) represents the occurrence of asynaptic event (i.e., release of neurotransmitter) when R_(i)(t) is anon-zero value, f[P_(i)(t)], or non-occurrence of a synaptic event whenR_(i)(t)=0 of and θ_(i) is a threshold potential for the ith dynamicsynapse. The synaptic signal R_(i)(t) causes generation of apostsynaptic signal, S_(i)(t), in a respective postsynaptic neuron bythe dynamic synapse. For convenience, f[P_(i)(t)] may be set to 1 sothat the synaptic signal R_(i)(t) is a binary train of spikes with 0sand 1s. This provides a means of coding information in a synapticsignal.

[0055]FIG. 2B is a block diagram illustrating signal processing of adynamic synapse with multiple internal synaptic processes. The dynamicsynapse receives an action potential 240 from a presynaptic neuron (notshown). Different internal synaptic processes 250, 260, and 270 areshown to have different time-varying magnitudes 250 a, 260 a, and 270 a,respectively. The synapse combines the synaptic processes 250 a, 260 a,and 270 a to generate a composite synaptic potential 280 whichcorresponds to the operation of Equation (1). A thresholding mechanism290 of the synapse performs the operation of Equation (2) to produce asynaptic signal 292 of binary pulses.

[0056] The probability of release of a synaptic signal R_(i)(t) isdetermined by the dynamic interaction of one or more internal synapticprocesses and the temporal pattern of the spike train of the presynapticsignal. FIG. 3A shows a presynaptic neuron 300 sending out a temporalpattern 310 (i.e., a train of spikes of action potentials) to a dynamicsynapse 320 a. The spike intervals affect the interaction of varioussynaptic processes.

[0057]FIG. 3B is a chart showing two facilitative processes of differenttime scales in a synapse. FIG. 3C shows two inhibitory dynamic processes(i.e., fast GABA_(A) and slow GABA_(B)). FIG. 3D shows the probabilityof release is a function of the temporal pattern of a spike train due tothe interaction of synaptic processes of different time scales.

[0058]FIG. 3E further shows that three dynamic synapses 360, 362, 364connected to a presynaptic neuron 350 transform a temporal spike trainpattern 352 into three different spike trains 360 a, 362 a, and 364 a toform a spatio-temporal pattern of discrete synaptic events ofneurotransmitter release.

[0059] The capability of dynamically tuning synaptic strength as afunction of the temporal pattern of neuronal activation gives rise to asignificant representational and processing power at the synaptic level.Consider a neuron which is capable of firing at a maximum rate of 100 Hzduring a time window of 100 ms. The temporal patterns that can be codedin this 10-bit spike train range from [00 . . . 0] to [11 . . . 1] to atotal of 2¹⁰ patterns. Assuming that at most one release event may occurat a dynamic synapse per action potential, depending on the dynamics ofthe synaptic mechanisms, the number of the temporal patterns that can becoded by the release events at a dynamic synapse is 2¹⁰. For a neuronwith 100 dynamic synapses, the total number of temporal patterns thatcan be generated is (2¹⁰)¹⁰⁰=2^(1,000). The number would be even higherif more than one release event is allowed per action potential. Theabove number represents the theoretical maximum of the coding capacityof neurons with dynamic synapses and will be reduced due to factors suchas noise or low release probability.

[0060]FIG. 4A shows an example of a simple neural network 400 having anexcitatory neuron 410 and an inhibitory neuron 430 based on the systemof FIG. 1 and the dynamic synapses of Equations (1) and (2). A total offour dynamic synapses 420 a, 420 b, 420 c, and 420 d are used to connectthe neurons 410 and 430. The inhibitory neuron 430 sends a feedbackmodulation signal 432 to all four dynamic synapses.

[0061] The potential of release, P_(i)(t), of ith dynamic synapse can beassumed to be a function of four processes: a rapid response, F₀, by thesynapse to an action potential A_(P) from the neuron 410, first andsecond components of facilitation F₁ and F₂ within each dynamic synapse,and the feedback modulation Mod which is assumed to be inhibitory.Parameter values for these factors, as an example, are chosen to beconsistent with time constants of facilitative and inhibitory processesgoverning the dynamics of hippocampal synaptic transmission in a studyusing nonlinear analytic procedures. See, Berger et al., “Nonlinearsystems analysis of network properties of the hippocampal formation”, in“Neurocomputation and learning: foundations of adaptive networks,”edited by Moore and Gabriel, pp.283-352, MIT Press, Cambridge (1991) and“A biologically-based model of the functional properties of thehippocampus,” Neural Networks, Vol. 7, pp.1031-1064 (1994).

[0062] FIGS. 4B-4D show simulated output traces of the four dynamicsynapses as a function of time under different responses of thesynapses. In each figure, the top trace is the spike train 412 generatedby the neuron 410. The bar chart on the right hand side represents therelative strength, i.e., K_(i,m) in Equation (1), of the four synapticprocesses for each of the dynamic synapses. The numbers above the barsindicate the relative magnitudes with respect to the magnitudes ofdifferent processes used for the dynamic synapse 420 a. For example, inFIG. 4B, the number 1.25 in bar chart for the response for F₁ in thesynapse 420 c (i.e., third row, second column) means that the magnitudeof the contribution of the first component of facilitation for thesynapse 420 c is 25% greater than that for the synapse 420 a. The barswithout numbers thereabove indicate that the magnitude is the same asthat of the dynamic synapse 420 a. The boxes that encloses releaseevents in FIGS. 4B and 4C are used to indicate the spikes that willdisappear in the next figure using different response strengths for thesynapses. For example, the rightmost spike in the response of thesynapse 420 a in FIG. 4B will not be seen in the corresponding trace inFIG. 4C. The boxes in FIG. 4D, on the other hand, indicate spikes thatdo not exist in FIG. 4C.

[0063] The specific functions used for the four synaptic processes inthe simulation are as follows. The rapid response, F₀, to the actionpotential, A_(p), is expressed as${{\tau_{F_{0}}\frac{F_{0}}{t}} = {{- F_{0}} + {k_{F_{0}}A_{P}}}},$

[0064] where τ_(F0)=0.5 ms is the time constant of F₀ for all dynamicsynapses and k_(F0)=10.0 is for the synapse 420 a and is scaledproportionally based on the bar charts in FIGS. 4B-4D for othersynapses.

[0065] The time dependence of F₁ is${{\tau_{f1}\frac{F_{1}}{t}} = {{- {F_{1}(t)}} + {k_{f1\_}A_{P}}}},$

[0066] where τ_(f1)=66.7 ms is the decay time constant of the firstcomponent of facilitation of all dynamic synapses and k_(f1)=0.16 forthe synapse 420 a.

[0067] The time dependence of F₂ is${{\tau_{f2}\frac{F_{2}}{t}} = {{- {F_{2}(t)}} + {k_{f2\_}A_{P}}}},$

[0068] where τ_(f2)=300 ms is the decay time constant of the secondcomponent of facilitation of all dynamic synapses and k_(f2)=80.0 forthe synapse 420 a.

[0069] The inhibitory feedback modulation is${{\tau_{Mod}\frac{{Mod}}{t}} = {{- {Mod}} + {k_{Mod\_}A_{Inh}}}},$

[0070] where A_(Inh) is the action potential generated by the neuron430, τ_(Mod)=10 ms is the decay time constant of the feedback modulationof facilitation of all dynamic synapses, and k_(Mod)=−20.0 is for thesynapse 420 a.

[0071] Equations (3)-(6) are specific examples of F_(i,m)(t) in Equation(1). Accordingly, the potential of release at each synapse is a sum ofall four contributions based on Equation (1):

P=F ₀ +F ₁ +F ₂+Mod.

[0072] A quanta Q (=1.0) of neurotransmitter is released if P is greaterthan a threshold θ_(R) (=1.0) and there is at least one quanta ofneurotransmitter in each synapse available for release (i.e., the totalamount of neurotransmitter, N_(total), is greater than a quanta forrelease). The amount of the neurotransmitter at the synaptic cleft,N_(R), is an example of R_(i)(t) in Equation (2). Upon release of aquanta of neurotransmitter, N_(R) is reduced exponentially with timefrom the initial amount of Q:${N_{R} = {Q\quad {\exp \left\lbrack {- \frac{t}{\tau_{0}}} \right\rbrack}}},$

[0073] where τ₀ is a time constant and is taken as 1.0 ms forsimulation. After the release, the total amount of neurotransmitter isreduced by Q.

[0074] There is a continuous process for replenishing neurotransmitterwithin each synapse. This process can be simulated as follows:${\frac{N_{Total}}{t} = {\tau_{rp}\left( {N_{\max} - N_{Total}} \right)}},$

[0075] where N_(max) is the maximum amount of available neurotransmitterand τ_(rp) is the rate of replenishing neurotransmitter, which are 3.2and 0.3 ms⁻¹ in the simulation, respectively.

[0076] The synaptic signal, N_(R), causes generation of a postsynapticsignal, S, in a respective postsynaptic neuron. The rate of change inthe amplitude of the postsynaptic signal S in response to an event ofneurotransmitter release is proportional to N_(R):${{\tau_{S}\frac{S}{t}} = {{- S} + {k_{S\_}N_{R}}}},$

[0077] where τ_(S) is the time constant of the postsynaptic signal andtaken as 0.5 ms for simulation and k_(s) is a constant which is 0.5 forsimulation. In general, a postsynaptic signal can be either excitatory(ks>0) or inhibitory (ks<0).

[0078] The two neurons 410 and 430 are modeled as “integrate-and-fire”units having a membrane potential, V, which is the sum of all synapticpotentials, and an action potential, A_(p) from a presynaptic neuron:${{\tau_{V}\frac{V}{t}} = {{- V} + {\sum\limits_{i}\quad S_{i}}}},$

[0079] where τ_(V) is the time constant of V and is taken as 1.5 ms forsimulation. The sum is taken over all internal synapse processes.

[0080] In the simulation, A_(p)=1 if V>θ_(R) which is 0.1 for thepresynaptic neuron 410 and 0.02 for the postsynaptic neuron 430. It alsoassumed that the neuron is not in the refractory period (T_(ref)=2.0ms), i.e., the neuron has not fired within the last T_(ref) of 2 ms.

[0081] Referring back to FIGS. 4B-4D, the parameter values for thesynapse 420 a is kept as constant in all simulations and is treated as abase for comparison with other dynamic synapses. In the first simulationof FIG. 4B, only one parameter is varied per terminal by an amountindicated by the respective bar chart. For example, the contribution ofthe current action potential (F₀) to the potential of release isincreased by 25% for the synapse 420 b, whereas the other threeparameters remain the same as the synapse 420 a. The results are asexpected, namely, that an increase in either F₀, F_(1, or F) ₂ leads tomore release events, whereas increasing the magnitude of feedbackinhibition reduces the number of release events.

[0082] The transformation function becomes more sophisticated when morethan one synaptic mechanism undergoes changes as shown in FIG. 4C.First, although the parameters remain constant in the synapse 420 a,fewer release events occur since an overall increase in the output fromthe other three synapses 420 b, 420 c, 420 d causes an increasedactivation of the postsynaptic neuron. This in turn exerts greaterinhibition of the dynamic synapses. This exemplifies how synapticdynamics can be influenced by network dynamics. Second, the differencesin the outputs from dynamic synapses are not merely in the number ofrelease events, but also in their temporal patterns. For example, thesecond dynamic synapse (420 b) responds more vigorously to the firsthalf of the spike train and less to the second half, whereas the thirdterminal (420 c) responds more to the second half. In other words, thetransform of the spike train by these two dynamic synapses arequalitatively different.

[0083] Next, the response of dynamic synapses to different temporalpatterns of action potentials is also investigated. This aspect has beentested by moving the ninth action potential in the spike train to apoint about 20 ms following the third action potential (marked by arrowsin FIGS. 4C and 4D). As shown in FIG. 4D, the output patterns of alldynamic synapses are different from the previous ones. There are somechanges that are common to all terminals, yet some are specific tocertain terminals only. Furthermore, due to the interaction of dynamicsat the synaptic and network levels, removal of an action potential (theninth in FIG. 4C) leads to a decrease of release events immediately, andan increase in release events at a later time.

[0084] The above discussion of the computational power of a neuralsystem with dynamic synapses is considered purely based on theoreticalgrounds, and the actual computational capacity of a given neural systemcertainly would be limited by certain practical biological constraints.For example, the representational capability of 2^(1,000) is based onthe assumption that a dynamic synapse is sensitive to the occurrence ornonoccurrence of a single action potential (i.e., each “bit”) in a spiketrain. In many practical situations, noise may corrupt an input spiketrain and thus can adversely affect the response of a neural network. Itis important to determine whether dynamic synapses are capable ofextracting statistically significant features from noisy spike trains.This problem is particularly acute in biology given that, to survive, ananimal must extract regularities from an otherwise constantly changingenvironment. For instance, a rat must be able to choose from a number ofpossible routes to navigate to its nest or to a food store. Thesepossible routes includes some novel routes and one or more certain givenroutes regardless of variations in a wide variety of conditions such aslighting, time of day, a cloud drifting by, a swaying tree, winds,odors, sounds, etc. Thus, neurons in the hippocampus must extractinvariants from varying input signals.

[0085] One aspect of the invention is a dynamic learning ability of aneural network based on dynamic synapses. Referring back to the system100 in FIG. 1, each dynamic synapse is configured according to a dynamiclearning algorithm to modify the coefficient, i.e., K_(i,m)(t) inEquation (1), of each synaptic process in order to find an appropriatetransformation function for a synapse by correlating the synapticdynamics with the activity of the respective postsynaptic neurons. Thisallows each dynamic synapse to learn and to extract certain feature fromthe input signal that contribute to the recognition of a class ofpatterns.

[0086] In addition, the system 100 of FIG. 1 creates a set of featuresfor identifying a class of signals during a learning and extractingprocess with one specific feature set for each individual class ofsignals.

[0087] One embodiment of the dynamic learning algorithm for mth processof ith dynamic synapse can be expressed as the following equation:

K _(i,m)(t+Δt)=K _(i,m)(t)+α_(m—) F _(i,m)(t)_(—) A _(Pj)(t)−β_(m—) [F_(i,m)(t)−F ⁰ _(i,m)],

[0088] where Δt is the time elapse during a learning feedback, α_(m) isa learning rate for the mth process, and A_(pj) (=1 or 0) indicates theoccurrence (A_(pj)=1) or non-occurrence (A_(pj)=0) of an actionpotential of postsynaptic neuron j that is connected to the ith dynamicsynapse, β_(m) is a decay constant for the mth process and F⁰ _(i,m) isa constant for mth process of ith dynamic synapse. Equation (12)provides a feedback from a postsynaptic neuron to the dynamic synapseand allows a synapse to respond according to a correlation therebetween.This feedback is illustrated by a dashed line 230 directed from thepostsynaptic neuron 220 to the dynamic synapse 210 in FIG. 2.

[0089] The above learning algorithm enhances a response by a dynamicsynapse to patterns that occur persistently by varying the synapticdynamics according to the correlation of the activation level ofsynaptic mechanisms and postsynaptic neuron. For a given noisy inputsignal, only the subpatterns that occur consistently during a learningprocess can survive and be detected by synaptic synapses.

[0090] This provides a highly dynamic picture of information processingin the neural network. At any state in a chain of informationprocessing, the dynamic synapses of a neuron extract a multitude ofstatistically significant temporal features from an input spike trainand distribute these temporal features to a set of postsynaptic neuronswhere the temporal features are combined to generate a set of spiketrains for further processing. From the perspective of patternrecognition, each dynamic synapse learns to create a “feature set” forrepresenting a particular component of the input signal. Since noassumptions are made regarding feature characteristics, each feature setis created on-line in a class-specific manner, i.e., each class of inputsignals is described by its own, optimal set of features.

[0091] This dynamic learning algorithm is broadly and generallyapplicable to pattern recognition of spatio-temporal signals. Thecriteria for modifying synaptic dynamics may vary according to theobjectives of a particular signal processing task. In speechrecognition, for example, it may be desirable to increase a correlationbetween the output patterns of the neural network between varyingwaveforms of the same word spoken by different speakers in a learningprocedure. This reduces the variability of the speech signals. Thus,during presentation of the same words, the magnitude of excitatorysynaptic processes is increased and the magnitude of inhibitory synapticprocesses is decreased. Conversely, during presentation of differentwords, the magnitude of excitatory synaptic processes is decreased andthe magnitude of inhibitory synaptic processes is increased.

[0092] A speech waveform as an example for temporal patterns has beenused to examine how well a neural network with dynamic synapses canextract invariants. Two well-known characteristics of a speech waveformare noise and variability. Sample waveforms of the word “hot” spoken bytwo different speakers are shown in FIGS. 5A and 5B, respectively. FIG.5C shows the waveform of the cross-correlation between the waveforms inFIGS. 5A and 5B. The correlation indicates a high degree of variationsin the waveforms of the word “hot” by the two speakers. The taskincludes extracting invariant features embedded in the waveforms thatgive rise to constant perception of the word “hot” and several otherwords of a standard “HVD” test (H-vowel-D, e.g., had, heard, hid). Thetest words are care, hair, key, heat, kit, hit, kite, height, cot, hot,cut, hut, spoken by two speakers in a typical research office with nospecial control of the surrounding noises (i.e., nothing beyond loweringthe volume of a radio). The speech of the speakers is first recorded anddigitized and then fed into a computer which is programmed to simulate aneural network with dynamic synapses.

[0093] The aim of the test is to recognize words spoken by multiplespeakers by a neural network model with dynamic synapses. In order totest the coding capacity of dynamic synapses, two constraints are usedin the simulation. First, the neural network is assumed to be small andsimple. Second, no preprocessing of the speech waveforms is allowed.FIG. 6A is schematic showing a neural network model 600 with two layersof neurons for simulation. A first layer of neurons, 610, has 5 inputneurons 610 a, 610 b, 610 c, 610 d, and 610 e for receiving unprocessednoisy speech waveforms 602 a and 602 b from two different speakers. Asecond layer 620 of neurons 620 a, 620 b, 620 c, 620 d, 620 e and 622forms an output layer for producing output signals based on the inputsignals. Each input neuron in the first layer 610 is connected by 6dynamic synapses to all of the neurons in the second layer 620 so thereare a total of 30 dynamic synapses 630. The neuron 622 in the secondlayer 620 is an inhibitory interneuron and is connected to produce aninhibitory signal to each dynamic synapse as indicated by a feedbackline 624. This inhibitory signal serves as the term “A_(inh)” inEquation (6). Each of the dynamic synapses 630 is also connected toreceive a feedback from the output of a respective output neuron in thesecond layer 620 (not shown).

[0094] The dynamic synapses and neurons are simulated as previouslydescribed and the dynamic learning algorithm of Equation (12) is appliedto each dynamic synapse. The speech waveforms are sampled at 8 KHz. Thedigitized amplitudes are fed to all the input neurons and are treated asexcitatory postsynaptic potentials.

[0095] The network 600 is trained to increase the cross-correlation ofthe output patterns for the same words while reducing that for differentwords. During learning, the presentation of the speech waveforms isgrouped into blocks in which the waveforms of the same word spoken bydifferent speakers are presented to the network 600 for a total of fourtimes. The network 600 is trained according to the following Hebbian andanti-Hebbian rules. Within a presentation block, the Hebbian rule isapplied: if a postsynaptic neuron in the second layer 620 fires afterthe arrival of an action potential, the contribution of excitatorysynaptic mechanisms is increased, while that of inhibitory mechanisms isdecreased. If the postsynaptic neuron does not fire, then the excitatorymechanisms are decreased while the inhibitory mechanisms are increased.The magnitude of change is the product of a predefined learning rate andthe current activation level of a particular synaptic mechanism. In thisway, the responses to the temporal features that are common in thewaveforms will be enhanced while that to the idiosyncratic features willbe discouraged. When the presentation first switches to the next blockof waveforms of a new word, the anti-Hebbian rule is applied by changingthe sign of the learning rates α_(m) and β_(m) in Equation (12). Thisenhances the differences between the response to the current word andthe response to the previous different word.

[0096] The results of training the neural network 600 are shown in FIGS.6B, 6C, 6D, 6E, and 6F, which respectively correspond to thecross-correlation functions of the output signals from neurons 620 a,620 b, 620 c, 620 d, and 620 e for the word “hot”. For example, FIG. 6Bshows the cross-correlation of the two output patterns by the neuron 620a in response to two waveforms of “hot” spoken by two differentspeakers. Compared to the correlation of the raw waveforms of the word“hot” in FIG. 5C which shows almost no correlation at all, each of theoutput neurons 620 a-620 e generates temporal patterns that are highlycorrelated for different input waveforms representing the same wordspoken by different speakers. That is, given two radically differentwaveforms that nonetheless comprises a representation of the same word,the network 600 generates temporal patterns that are substantiallyidentical.

[0097] The extraction of invariant features from other test words byusing the neural network 600 are shown in FIGS. 7A-7L. A significantincrease in the cross-correlation of output patterns is obtained in alltest cases.

[0098] The above training of a neural network by using the dynamiclearning algorithm of Equation (12) can further enable a trained networkto distinguish waveforms of different words. As an example, the neuralnetwork 600 of FIG. 6A produces poorly correlated output signals fordifferent words after training.

[0099] A neural network based on dynamic synapses can also be trained incertain desired ways. A “supervised” learning, for example, may beimplemented by training different neurons in a network to respond onlyto different features. Referring back to the simple network 600 of FIG.6A, the output signals from neurons 602 a (“N1”), 602 b (“N2”), 602 c(“N3”), and 602 d (“N4”) may be assigned to different “target” words,for example, “hit”, “height”, “hot”, and “hut”, respectively. Duringlearning, the Hebbian rule is applied to those dynamic synapses of 630whose target words are present in the input signals whereas theanti-Hebbian rule is applied to all other dynamic synapses of 630 whosetarget words are absent in the input signals.

[0100]FIGS. 8A and 8B show the output signals from the neurons 602 a(“N1”), 602 b (“N2”), 602 c (“N3”), and 602 d (“N4”) before and aftertraining of each neuron to respond preferentially to a particular wordspoken by different speakers. Prior to training, the neurons respondidentically to the same word. For example, a total of 20 spikes areproduced by every one of the neurons in response to the word “hit” and37 spikes in response to the word “height”, etc. as shown in FIG. 8A.After training the neurons 602 a, 602 b, 602 c, and 602 d to preferablyrespond to words “hit”, “height”, “hat”, and “hut”, respectively, eachtrained neuron learns to fire more spikes for its target word than otherwords. This is shown by the diagonal entries in FIG. 8B. For example,the second neuron 602 b is trained to respond to word “height” andproduces 34 spikes in presence of word “height” while producing lessthan 30 spikes for other words.

[0101] The above simulations of speech recognition are examples oftemporal pattern recognition in the more general temporal signalprocessing where the input can be either continuous such as a speechwaveform, or discrete such as time series data. FIG. 9A shows oneimplementation of temporal signal processing using a neural networkbased on dynamic synapses. All input neurons receive the same temporalsignal. In response, each input neuron generates a sequence of actionpotentials (i.e., a spike train) which has a similar temporalcharacteristics to the input signal. For a given presynaptic spiketrain, the dynamic synapses generate an array of spatio-temporalpatterns due to the variations in the synaptic dynamics across thedynamic synapses of a neuron. The temporal pattern recognition isachieved based on the internally-generated spatio-temporal signals.

[0102] A neural network based on dynamic synapses can also be configuredto process spatial signals. FIG. 9B shows one implementation of spatialsignal processing using a neural network based on dynamic synapses.Different input neurons at different locations in general receive inputsignals of different magnitudes. Each input neuron generates a sequenceof action potentials with a frequency proportional the to the magnitudeof a respective received input signal. A dynamic synapse connected to aninput neuron produces a distinct temporal signal determined byparticular dynamic processes embodied in the synapse in response to apresynaptic spike train. Hence, the combination of the dynamic synapsesof the input neurons provide a spatio-temporal signal for subsequentpattern recognition procedures.

[0103] It is further contemplated that the techniques and configurationsin FIGS. 9A and 9B can be combined to perform pattern recognition in oneor more input signals having features with both spatial and temporalvariations.

[0104] The above described neural network models based on dynamicsynapses can be implemented by devices having electronic components,optical components, and biochemical components. These components mayproduce dynamic processes different from the synaptic and neuronalprocesses in biological nervous systems. For example, a dynamic synapseor a neuron may be implemented by using RC circuits. This is indicatedby Equations (3)-(11) which define typical responses of RC circuits. Thetime constants of such RC circuits may be set at values that differentfrom the typical time constants in biological nervous systems. Inaddition, electronic sensors, optical sensors, and biochemical sensorsmay be used individually or in combination to receive and processtemporal and/or spatial input stimuli.

[0105] Although the present invention has been described in detail withreference to the preferred embodiments, various modifications andenhancements may be made without departing from the spirit and scope ofthe invention. For example, Equations (3)-(11) used in the examples haveresponses of RC circuits. Other types of responses may also be used suchas a response in form of the a function: G(t)=α²te^(−αt), where α is aconstant and may be different for different synaptic processes. Foranother example, various different connecting configurations other thanthe examples shown in FIGS. 9A and 9B may be used for processingspatio-temporal information. FIG. 10 shows another embodiment of aneural network based on dynamic synapses. In yet another example, thetwo-state model for the output signal of a dynamic synapse in Equation(2) may be modified to produce spikes of different magnitudes dependingon the values of the potential for release. These and other variationsare intended to be encompassed by the following claims.

What is claimed is:
 1. A system for information processing, comprising:a plurality of signal processing elements connected to communicate withone another and configured to produce at least one output signal inresponse to at least one input signal; and a plurality of processingjunctions disposed to interconnect said plurality of signal processingelements to form a network, wherein each of said processing junctionsreceives and processes a prejunction signal from a first signalprocessing element in said network based on at least one internaljunction process to produce a junction signal that constantly varieswith at least one parameter of said prejunction signal.
 2. A system forinformation processing, comprising a signal processor and a processingjunction connected to communicate with each other to process an inputsignal received by said processing junction, wherein said processingjunction has at least one internal junction process which responds tosaid input signal to produce a junction signal that continuously changesaccording to a temporal change in said input signal and said signalprocessor is operable to produce an output signal in response to saidjunction signal.